Question 7 - A-Level Maths

The complex number \(3 + 2 \mathrm { i }\) is denoted by \(w\) and the complex conjugate of \(w\) is denoted by \(w ^ { * }\). Find
1. the modulus of \(w\),
2. the argument of \(w ^ { * }\), giving your answer in radians, correct to 2 decimal places.
Find the complex number \(u\) given that \(u + 2 u ^ { * } = 3 + 2 \mathrm { i }\).
Sketch, on an Argand diagram, the locus given by \(| z + 1 | = | z |\).